Solving the strong CP problem without axions

TL;DR

This paper proposes a novel solution to the strong CP problem through spontaneous CP violation, utilizing specific quark-mass textures and symmetry principles in supersymmetric theories, avoiding the need for axions.

Contribution

It introduces a new framework for solving the strong CP problem via spontaneous CP violation with specific quark-mass textures and symmetry realizations in supersymmetric models.

Findings

Conditions for spontaneous CP violation to solve the strong CP problem.

Realizations using modular invariance or local U(1) symmetry.

Models with small modular weights and higher levels N=2 or N=3.

Abstract

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavour symmetry, suggesting a unified solution to the strong CP problem and the flavour puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights $\pm2$ ($\pm1$), utilising higher levels $N=2$ ($N=3$). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavour group.